Question: $f(x) = -2x^{2}+1$ What is the range of $f(x)$ ?
Consider the range of $-2x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $-2$ flips the range to $\{\, y \mid y \le 0 \,\}$ To get $-2x^{2}+1$, we add $1$.